Step 1If using xanthan gum: In a blender, combine the water, lemon juice, sugar, salt and hazelnut oil. Turn the mixer on medium-low speed until a vortex forms in the center of the liquid. Slowly drizzle the xanthan gum into the vortex and blend until thoroughly combined, about 1 minute.
Step 2If using gelatin: Bloom the gelatin sheet in ice water. Combine the water, lemon juice, sugar, salt and hazelnut oil in a small saucepan. Gently warm the mixture to a slight simmer, then add the bloomed gelatin. Whisk until the gelatin is dissolved and thoroughly incorporated. Strain and chill.
Step 3Strain the vinaigrette through a chinois, cover and chill until just before serving. This makes about 1 1/4 cups vinaigrette. Garnish with the chives just before serving.